<p>12.If x is a positive integer is x^7=k and x^9=m, which of the following must be equal to x^11?</p>
<p>(A) m²/k
(B) m²-k
(C) m²-7
(D) 2k-m/3
(E) k+4</p>
<p>Please Note: This is from the 2007-2008 official SAT practice test.</p>
<p>Any help is appreciated. Thanks!</p>
<p>Why not simply substitute numbers?</p>
<p>2^7 = 128</p>
<p>2^9 = 512</p>
<p>OK then, m = 512, and k = 128.</p>
<p>Now, what is 2^11? The answer is 2048.</p>
<p>Therefore, by plugging m and k, 512 and 128, respectively, you will arrive at the correct answer from trying the first answer choice.</p>
<p>Time taken: 10-20 seconds. My math score is 780.</p>
<p>Key for this problem: See how you can split 11 into 9 and 7, then substitute.</p>
<p>x^11= x^(18-7)= (x^18)/(x^7) = ((x^9)^2)/(x^7) = (m^2)/k or A</p>
<p>Time taken: <10 seconds</p>
<p>If you’re good with algebra, then I suggest you follow cortana431’s solution. But I hate algebra, and I always fail with it; instead, I substitute numbers. Not only does this solution require such a little amount of time, but it is flawless. There are no rules to follow, no substituting ‘principles’ or mistakes you can make in the middle, as with algebra (such as taking a number to the other side of an equation and forgetting to put it in negative/positive form). Go with what suits you best.</p>
<p>For this question too, you can pretty much glance at the problem and see that the answer MUST be A. If you look at choices B,C,D, and E, you can see that the operations performed can in no way yield a great exponent, x^11 (i.e multiplying by 2, adding and subtracting (all of which are not exponent properties). So another solution is by doing this and seeing that A is the only plausible answer.</p>